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If it fits in both corridors without reorientiation, it follows that it fits through the corner, which is part of both corridors. (Imagine sliding a square on a chessboard.) Or are you asking something more complicated? Is that ascii drawing supposed to be to scale?

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While this is always true, it is possible to get a longer object in if you turn as you go. It's an easy problem if the object has no thickness, but trickier otherwise.

To solve the problem for an object with thickness, imagine shifting the wall on the inside of the turn in by a distance equal to the width of a box (with the corner expanding out to a semicircle), and then consider moving a line segment through the appropriately shrunken hallway.

Note that we're still being possibly inefficient, as we are not using our third available dimension; however, this is only relevant if the box is much longer in one direction than the other two (for example, if you were trying to carry a 2x4 around this corner).

Yes, I understand that. That's why I asked if his drawing was supposed to be to scale.

he might be implying somehow that one or more people are carrying it, which might require rotation.

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